This invention relates generally to modulating volume samples in a rendering pipeline, and more particularly, to modulating lighting values using gradient magnitude vectors and complex functions.
Introduction to Volume Rendering
Volume rendering is often used in computer graphics applications where three-dimensional data need to be visualized. The volume data can be scans of physical or medical objects, or atmospheric, geophysical, or other scientific models where visualization of the data facilitates an understanding of the underlying real-world structures represented by the data.
With volume rendering, the internal structure, as well as the external surface features of physical objects and models are visualized. Voxels are usually the fundamental data items used in volume rendering. A voxel is a data item that represents a particular three-dimensional portion of the object or model. The coordinates (x, y, z) of each voxel map the voxels to positions within the represented object or model.
A voxel represents some particular intensity value of the object or model. For a given volume, intensity values can be physical parameters, such as, density, tissue type, elasticity, velocity, to name but a few. During rendering, the voxel values are converted to color and opacity (rgba) values which can be projected onto a two-dimensional image plane for viewing.
One frequently used technique during rendering is ray-casting. A set of imaginary rays are cast through the array of voxels. The rays originate from a viewer""s eye or from an image plane. The voxel values are re-sampled to points along the rays, and various techniques are known to convert the sampled values to pixel values. In particular, voxel values may be converted directly to rgba voxels, which are then re-sampled along rays and accumulated to pixel values. In either case, processing may proceed back-to-front, or front-to-back.
Rendering Pipeline
Volume rendering can be done by software or hardware. In one hardware implementation, the hardware is arranged as a multi-stage pipeline, see U.S. patent application Ser. No. 09/190,643 xe2x80x9cFast Storage and Retrieval of Intermediate Values in a Real-Time Volume Rendering System,xe2x80x9d filed by Kappler et al. on Nov. 12, 1998.
Illumination
Illumination is well-known in both art and computer graphics for increasing the realism of an image by adding highlights, reflections, and shadows, thereby appealing to one of the natural capabilities of the human eye to recognize three-dimensional objects. A number of prior art illumination techniques are known in computer graphics, generally involving complex calculations among the directions to each of the light sources, normal vectors to surfaces, and the position of the viewer. In polygon graphics systems, where the three-dimensional objects are depicted by partitioning their surfaces many small triangles, the normal at each point on a surface is easily obtained from the specification of the triangle containing that point.
Naturally, it is a challenge for any graphics system to carry out these calculations quickly enough for real-time operation. One technique for performing them efficiently is described by Voorhies et al. in xe2x80x9cReflection Vector Shading Hardware,xe2x80x9d Computer Graphics Proceedings, Annual Conference Series, pp. 163-166, 1994. They describe a polygon graphics system in which the calculations involving the eye vector and light sources are partially pre-computed for a fixed set of directions and stored in lookup tables. During rendering, reflection vectors are used to index into these tables to obtain values for modulating the intensities of the red, green, and blue colors assigned to the points on the surfaces of the objects depicted in the image. The only calculations necessary in real-time are for obtaining reflection vectors themselves and for applying the modulation.
Applying illumination in volume graphics is more difficult because there are rarely any defined surfaces in a volume data set. Instead, visible surfaces must be inferred from the data itself, as discussed by Levoy in xe2x80x9cDisplay of Surfaces From Volume Data,xe2x80x9d IEEE Computer Graphics and Applications, May, 1988, pp. 29-37. A common technique is to calculate gradients throughout the volume data set, that is the rates and directions of change of the voxel values with respect to position. At points where the gradient is strong, a surface or boundary between material types can be inferred, with the gradient pointing in the direction opposite to the normal of the surface. The magnitude of the gradient indicates the sharpness of the surface. In other words, where the surface is xe2x80x9cfuzzy,xe2x80x9d the magnitude is a measure of the likelihood of the surface. Traditional illumination techniques are then applied to modulate the color intensity and alpha values according to both the magnitude and direction of the gradient at each point in the volume, for example as described by Drebin, et al., in xe2x80x9cVolume Rendering,xe2x80x9d Computer Graphics, August 1988, pp. 65-74. By this method, features which exhibit high gradient magnitudes are accentuated as surfaces, while features which exhibit low gradient magnitudes are suppressed.
Terwisschavan van Scheltinga et al. in xe2x80x9cDesign of On-Chip Reflectance Map,xe2x80x9d Eurographics 95 Workshop on graphics Hardware, pp. 51-55, 1995, describe an application of the technique of Voorhies et al. to volume rendering. In that technique, specular and diffuse intensities are pre-computed based on directions to light sources and the eye of the viewer. The intensities are then stored in lookup tables called reflectance maps. Gradient vectors are used to index into these tables to obtain the intensities for modulating rgba values at sample locations in order to produce specular and diffuse highlights.
The above illumination techniques suffer from an inability to distinguish object surfaces from noise. Meaningful illumination can only take place when the samples can unequivocally be classified as surface or non-surface samples. Prior illuminators are inadequate because the presence of noise can cause them to assign strong illumination to voxels within homogeneous material. Neither Voorhies nor van Scheltinga suggest, teach or show illumination in a pipelined manner. Furthermore, the above techniques suffer a performance penalty in having to reload the reflectance maps anytime a view on an object changes. They do suggest computing a specular reflection vector on-the-fly, based on the gradient and eye vectors, which would obviate the need to reload the specular reflectance map when the view direction changes.
Gradient Magnitude Approximation
In the past, the brute force approach to determining gradient magnitudes included obtaining the sum of the squares of the gradient vector components (u,v,w) of the gradient vector Guvw, then deriving the square root of the this sum. This computation can be extremely hardware intensive, so software is often used. This is because the number of iterations necessary in doing a traditional square root calculation can be on the order of tens of steps.
The hardware necessary and the time allotted for such calculations is exceedingly complex and long, especially in view of a requirement for a real-time volume rendering, that needs to render at a rate of more than 500 million samples per second. Another prior art method for deriving gradient magnitude is by utilizing look-up tables, which suffers from the problem of the large number of gates required for any reasonable level of precision.
After having derived gradient magnitudes, it is desirable to provide the user with the ability to use the gradient magnitude to interactively modify the application of lighting or a sample""s opacity. This gives the user the ability to accentuate certain features, the ability to cut out certain features, or the ability to create a wide variety of alterations to the rendered object.
It is desired to improve on these prior art deficiencies while illuminating volume data. More particularly, it is desired to perform efficient and flexible illumination as a stage of a hardware pipeline.
The invention provides a method for modulating samples in a volume rendering pipeline by storing modulation values as entries in a table. Also stored are a grain and a base for the entries of the table to specify an index range.
A magnitude of a gradient vector of a sample is determined. The table is indexed using the magnitude to determine two modulation values corresponding to the magnitude. The two modulation values are interpolated using the grain and the base to determine a modulation factor to modulate the sample with a linear function.